PHOTODIODES - FROM
FUNDAMENTALS TO
APPLICATIONS
Edited by Ilgu Yun
Photodiodes - From Fundamentals to Applications
/>Edited by Ilgu Yun
Contributors
Toshiaki Kagawa, Volodymyr Tetyorkin, Andriy Sukach, Andriy Tkachuk, Mikhail Nikitin, Viacheslav Kholodnov,
Fernando de Souza Campos, José Alfredo Covolan Ulson, José Eduardo Cogo Castanho, Paulo Roberto De Aguiar,
Yong-Gang Zhang, Yi Gu, Iftiquar Sk, Lung-Chien Chen, Ana Luz Muñoz, Joaquin Campos Acosta, Alejandro Ferrero
Turrion, Alicia Pons Aglio, Aryan Afzalian, Sergey Dvoretsky, Vladimir Vasilyev, Vasily Varavin, Igor Marchishin, Nikolai
Mikhailov, Alexander Predein, Irina Sabinina, Yuri Sidorov, Alexander Suslyakov, Aleksandr Aseev
Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia
Copyright © 2012 InTech
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of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published
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Publishing Process Manager Romina Skomersic
Technical Editor InTech DTP team
Cover InTech Design team
First published December, 2012
Printed in Croatia

Chapter 5 Photodiodes as Optical Radiation Measurement Standards 173
Ana Luz Muñoz Zurita, Joaquín Campos Acosta, Alejandro Ferrero
Turrión and Alicia Pons Aglio
Section 3 Device Applications 193
Chapter 6 Si-Based ZnO Ultraviolet Photodiodes 195
Lung-Chien Chen
Chapter 7 Infrared Photodiodes on II-VI and III-V Narrow-Gap
Semiconductors 215
Volodymyr Tetyorkin, Andriy Sukach and Andriy Tkachuk
Chapter 8 Al(Ga)InP-GaAs Photodiodes Tailored for Specific
Wavelength Range 261
Yong-gang Zhang and Yi Gu
Chapter 9 Single- and Multiple-Junction p-i-n Type Amorphous Silicon
Solar Cells with p-a-Si1-xCx:H and nc-Si:H Films 289
S. M. Iftiquar, Jeong Chul Lee, Jieun Lee, Juyeon Jang, Yeun-Jung
Lee and Junsin Yi
Section 4 Circuit Applications 313
Chapter 10 Noise Performance of Time-Domain CMOS Image Sensors 315
Fernando de S. Campos, José Alfredo C. Ulson, José Eduardo C.
Castanho and Paulo R. Aguiar
Chapter 11 Design of Multi Gb/s Monolithically Integrated Photodiodes
and Multi-Stage Transimpedance Amplifiers in Thin-Film SOI
CMOS Technology 331
Aryan Afzalian and Denis Flandre
ContentsVI
Preface
This book represents recent progress and development of the photodiodes including the
fundamental reviews and the specific applications developed by the authors themselves.
The key idea of this book is that it allows authors to deal with a wide range of backgrounds
and recent research progresses in photodiode-related areas.

amplifier is surveyed.
In presenting this book, I would like to express my thanks to the authors who participate in
writing for each book chapter and followed my construct comments, constructive criticism,
and useful suggestions. They include: Toshiaki Kagawa, Viacheslav Kholodnov, Mikhail Ni‐
kitin, Sergey Dvoretsky, S. M. Iftiquar, V.V. Vasiliev, Ana Luz Muñoz Zurita, Lung-Chien
Chen, Volodymyr Tetyorkin, Yong-Gang Zhang, Fernando de S. Campos, Iftiquar Sk, Aryan
Afzalian, and others.
I especially wish to express my sincere thanks to Ms. Romina Skomersic, Publishing Process
Manager in InTech-Open Access Publisher, for the valuable publishing suggestions. More‐
over, I wish to thank the InTech-Open Access Publisher for helping in the typing adjustment
and for revising the English text for each book chapter.
Finally, I would like to thank for my wife, Hyun Jung Cha, and my two adorable sons, Jiho
and Joonho Yun, for their sincere care and support during the whole summer of 2012.
Ilgu Yun
School of Electrical and Electronic Engineering,
Yonsei University
PrefaceVIII
Section 1
Fundamental Physics and Physical Design

Chapter 1
Two-Photon Absorption in Photodiodes
Toshiaki Kagawa
Additional information is available at the end of the chapter
/>1. Introduction
Incident light with a photon energy ℏω induces two-photon absorption (TPA) when
E
g
/
2ℏωE

elements obtained from the self-TPA analysis.
Cross-TPA can be applied to polarization measurements. Photocurrents generated in the Si-
PD by cross-TPA between asignal light under test and a reference light are used to detect the
polarization. The light under test is arbitrarily polarized and its Jones vector can be deter‐
mined by photocurrents generated by cross-TPA. This measurement method can detect the
instantaneous polarization when the reference light temporally overlaps with the light un‐
der test. Because the time division is limited only by the pulse width of the reference light, it
is possible to detect rapid variationsin the polarization. This method can measure not only
the linear polarization direction but also the elliptical polarization. Applications to measure‐
ment of the output optical pulse from an optical fiber with birefringence and a semiconduc‐
tor optical amplifier are demonstrated.
2. TPA in semiconductors with diamond and zinc-blende crystals
2.1. Polarization dependence
TPA is a third-order nonlinear optical process. Third order nonlinear polarization is induced
by the optical electric field according to
P
i
(3)
(ω
i
, k
i
)=
1
4
ε
0
∑
j,k,l
χ

elements, the number of
non-zero independent elements is limited by the crystal symmetry and the properties of the
incident light. It is apparent that relations χ
xxxx
= χ
yyyy
= χ
zzzz
and χ
xxyy
= χ
xxzz
= χ
yyzz
, etc. hold
for a cubic crystal. Elements like χ
xxxy
andχ
xxyz
will be zero for crystals with 180° rotational
symmetry about a crystal axis. For degenerate TPA in which one or two parallel optical
beams with the same optical frequency propagate,ω
i
= −ω
j
=ω
k
=ω
l
and χ

are the electric field strengths andp
^
ande
^
are the polarization unit vectors of
the two beams. For circular or elliptical polarization, p
^
and e
^
are complex to express the
phase difference between the electric field oscillations along two axes. The nonlinear polari‐
zation along the polarization vector p
^
is given by
P
p
(3)
=
1
4
ε
0
(E
p
3
∑
i, j,k,l
p
i
*

wherep
i
and e
i
are elements of p
^
ande
^
, andp
i

*
and e
i

*
are their complex conjugate, respec‐
tively. Because there are only three nonzero independent tensor elements, the nonlinear po‐
larization can be written as [7]
P
p
(3)
=
1
4
ε
0
{
E
p

|
p
^
⋅e
^
|
2
+ χ
xyyx
(1 +
|
p
^
*
⋅e
^
|
2
) + σχ
xxxx
∑
i
|
p
i
|
2
|
e
i

pp
I
p
2
−β
pe
I
p
I
e
(6)
where I
p
and I
e
are optical intensity densities of the two beams. The absorption coefficient is
proportional to the imaginary part of the nonlinear polarization given in Eq. (4).
Two-Photon Absorption in Photodiodes
/>5
β
pp
=
ω
2n
2
c
2
ε
0
(χ

ω
n
2
c
2
ε
0
(χ
″
xxyy
|
p
^
⋅e
^
|
2
+ χ
″
xyyx
(1 +
|
p
^
*
⋅e
^
|
2
) + σ

″
xxxx
−χ
″
xxyy
−2χ
″
xyyx
χ
″
xxxx
(9)
2.2. Estimate of photocurrent induced by TPA in PDs
Commercially available PDs are usually designed to be used for photon energies greater
than the band gap of the photoabsorption layer. As the absorption coefficient is about 10
5
cm
-1
, absorption layer is several micrometers thick. On the other hand, the absorption coeffi‐
cient is much smaller for TPA. If we consider only self-TPA, Eq. (6) is solved as
I
p
(z)=
I
0
β
pp
I
0
z + 1

−6
μm
-1
. Because only a very small fraction of the incident light is absorbed
in PD with a photo-absorption layer that is several micrometers thick, the induced photocur‐
rent is proportional to the absorption coefficient β.
When optical pulses with an intensity density I
0
and pulse width T
p
are irradiated at a repe‐
tition rate of R, the induced photocurrent will be
J =ηβ
pp
I
0
2
S d T
p
R
q
ℏω
(11)
where η is the internal efficiency of the PD, d is the absorption layer thickness, and S is the
area of the incident beam. The photocurrent is estimated to be about 10
-8
A assuming that
Photodiodes - From Fundamentals to Applications6
the light intensity of 10
7

meter was placed at the location of the PD and it was used to check if the optical power was
independent of the polarization.
When two optical beams are illuminated on a PD, photocurrents due to self-TPA and cross-
TPAare simultaneously generated. It is necessary to detect only the photocurrent generated
by the cross-TPA. Optical pulse streams were mechanically chopped at frequencies of 1.0
and 1.4 kHz. Electrical pulsesthat had been synchronized with mechanical choppers were
fed into a mixer circuit that generated a sumfrequency of 2.4 kHz. These generated electrical
pulses with the sum frequency were used as the reference signal for the lock-in amplifier.
Thus, the lock-in amplifier detected only the photocurrent generated by two-beam absorp‐
tion, that is, cross TPA.
Two-Photon Absorption in Photodiodes
/>7
Figure 1. Measurement setup (LD: laser diode; NDF: normal dispersion fiber; ADF: abnormal dispersion fiber; PBS: po‐
larization beam splitter; PIBS: polarization independent beam splitter). The inset shows the rotation of the wave plate.
Light from the PBS is linearly polarized along the x axis,which is parallel tothe [1] axis of the PD.
4. Pulse width measurement by cross-TPA
Cross-TPA was used to measure the pulse width generated by the pulse compression proc‐
ess described in the previous section. After the compressed optical pulse was divided into
two branches by an optical fiber beam splitter, the timing between them was controlled by a
variable delay line. They were then irradiated on the Si-PD. The two beams were made or‐
thogonally linearly polarized to suppress noise due to interference. The photocurrent gener‐
ated by cross-TPA between the divided two optical beams is
J (τ)=β
∫
h (t)h (t −τ)dt
(12)
where h(t) is the pulse shape, and τ is the time delay between the two pulses. The pulse
width can be estimated by this self-correlation trace.
Figure 2 shows the self-correlation trace of the compressed optical pulse. The photocurrent
due to the cross-TPA is generated only when the two optical pulses temporally overlap on

cosθ −sinθ
sinθ cosθ
)
(
1 0
0
e
iφ
)
(
cosθ sinθ
−sinθ cosθ
)(
1
0
)
(13)
where ϕ=π and π/2 for half- and quarter-wave plates, respectively. The inset of Fig. 1 shows
the definition of the rotation angle. The principal axes of the quarter-wave plate are repre‐
sented by the X- and Y-axes. The phase of the polarization component along the Y-axis is
delayed by ϕ relative to that along the X-axis.
The anisotropy of self-TPA for linearly polarized light was measured for Si- and GaAs-PDs.
The crystal axis [001] is made parallel to the x-axis. The linear polarization is rotated by a
half-wave plate (i.e., ϕ=π in Eq. (13)). When the X-axis is tilted by an angle of θ relative to
the x-axis, the polarization direction of the output light from the half-wave plate is tilted by
Two-Photon Absorption in Photodiodes
/>9
2θ. Thus, the polarization is parallel to the [001] and [011] directions when the rotation angle
of the half-wave plate is θ = 0 and 22.5° , respectively. Using Eq. (7), the anisotropy parame‐
ter σ" defined by Eq. (9) can be written as

rameter σ'' is estimated to be –0.45. From Eqs. (7), (9) and (13), the dependence of the TPA
probability on the rotation angle θof the half-wave plate can be written as
β
pp
L
∝
1
4
χ
″
xxxx
(4−σ
″
+ σ
″
cos8θ)
(15)
The solid line in Fig. 3 (a) shows the value calculated using Eq. (15) and σ''= –0.45. In con‐
trast, the Si-PD exhibits negligibly small dependence on the polarization direction and the
TPA coefficient is almost isotropic;
|
σ
″
|
is estimated to be less than 0.04.
Figure 4(a) and (b) respectively shows the dependence of the photocurrents generated in the
GaAs- and Si-PDs on the rotation angle of a quarter-wave plate (ϕ=π/2in Eq. (13)). The inci‐
dent light is linearly polarized along the [001] direction and circularly polarized at θ = 0 and
Photodiodes - From Fundamentals to Applications10
45° , respectively. The difference in the self-TPA coefficients for linear and circular polariza‐

the results calculated using Eq. (17) and the parameters in Table 1.
The ratios χ ''
xxyy
/ χ ''
xxxx
and χ ''
xyyx
/ χ ''
xxxx
can be estimated from measured anisotropic
and dichroism parameters. Table 1 lists the obtained ratios for the nonlinear susceptibility
tensor elements for GaAs and Si.
From Eqs. (7), (9), (13) and (16), the dependence of the TPA coefficient on the quarter-wave
plate rotation angle θ is given by
β
pp
∝
1
16
χ
″
xxxx
(16−σ
″
−8δ + σ
″
cos8θ + 8δcos4θ)
(17)
This self-TPA coefficient is maximized when
cos

/
χ
″
xxxx
in Ta‐
ble 1, indicating that thepolarization dependence of the GaAs-PD is consistent with the
analysis based on the nonlinear susceptibility.
On the other hand, the photocurrent generated in the Si-PD is maximized when the an‐
gle is 0 and the incident light is linearly polarized, which contrasts the situation for the
GaAs PD. Because the anisotropy parameter is small, Eq. (18) does not hold at any rota‐
tion angle θ.
6. Discussion of self-TPA polarization dependence
The polarization dependence of self-TPA is strongly dependent on the crystal symmetry and
the band structure. Hutchings and Wherettcalculated nonlinear susceptibility tensor ele‐
ments based on kp perturbation [9]. The ratios listed in Table 1 are consistent with their re‐
sults. Murayamaand Nakayama[10] have performed ab initio calculations.Their calculated
values for the ratiosχ"
xxyy
/ χ"
xxxx
andχ"
xyyx
/ χ"
xxxx
depend on the photon energy. The val‐
ues of ratios shown in Table 1 are very similar to those calculated for a photon energy of 1
eV. The small discrepancy between the photon energies is probably due to the parameters
used in the calculation.
GaAs Si
Anisotropy parameter σ" -0.45

, Γ
1c
, and Γ
15c
are irreducible representations of the
point group T
d
(4
¯
3m) of the GaAs crystal for the highest valence band, the lowest conduction
band, and the higher conduction band at the Γ point, respectively [11]. The first transition
Γ
15v
→Γ
15c
occurs between p-like states, the second transition Γ
15c
→Γ
1c
occurs between p-like
Photodiodes - From Fundamentals to Applications12
and s-like states. The polarization directions that induce the first and second transitions
must be different from each other. For example, transitions
|
p
z
(Γ
15v
) →
|

1c
) are wave functions of each band [11]. This proc‐
ess does not contribute to χ
″
xxxx
andχ
″
xxyy
, but it contributes to χ
″
xyyx
causing the anisotropy
parameter σ’’ to be non-zero [7]. The matrix element of the optical dipole moment between
Γ
15v
and Γ
15c
is non-zero because T
d
lacks space inversion symmetry.
On the other hand, Si has the indirect transition type band structure. Figure 5(b) schemati‐
cally shows the band structure and the irreducible representation of this space group [11,12].
A photon energy of 0.8 eV is too small to induce a direct TPA transition without phonon
absorption or emission at any point in the first Brillouin zone of Si. The final sate of the TPA
transition is Δ
1
, which has the minimum energy of the conduction band. Many complicated
transitionsequences that include optical and phonon transitions exist to reach the final point
Δ
1

When a phonon process occurs after the first optical transition, the polarization effect of the
first optical transition on the intermediate state of TPA can be destroyed by the phonon
process. The anisotropy is thus considered to be reduced by this process.
7. Cross-TPA in Si-APD
As shown in the previous section, TPA in Si is isotropic. Thus, TPA in Si-PD is simpler than
that in GaAs-PD. In addition, a Si avalanche photodiode (APD) with the multiplication gain
is commercially available. Consequently, we concentrate on cross-TPA in Si-APD.
Cross-TPA depends on the relationship between the polarization vectors of the two beams.
We measure three cases: when both beams are linearly polarized, when one optical beam is
linearly polarized and the other is varied between linear, elliptical, and circular polarization
by a quarter-wave plate, and when one beam is circularly polarized and the other is varied
between linear, elliptical, and circular polarization [13].
Figure 6. Photocurrent due to cross- TPA between two linearly polarized beams. Solid line is the calculated results
using parameters in Table 1.
Figure 6 shows the photocurrent when both beams are linearly polarized. The horizon‐
tal axis of the figure is the rotation angle of the half- wave plate. The photocurrent was
Photodiodes - From Fundamentals to Applications14
normalized using the minimum photocurrent. The photocurrent is strongly dependent on
the orientation of the two linear polarization axes and has a maximum and minimum
values when the polarization axes of the two optical pulses are parallel and perpendicu‐
lar, respectively.
Equation (8) can be written as
β
pe
∝
1
2
(χ
″
xxyy

pe
(p
^
⊥e
^
)
=2 +
χ
″
xxyy
χ
″
xyyx
(20)
Using the parameters in Table 1 which were obtained from the self-TPA of Si, this ratio is
3.26. This value is consistent with the measured cross-TPA shown in Fig 6
Figure 7. Photocurrent due to cross-TPA between linear polarized and elliptical polarized lights. Solid line is the calcu‐
lated results using parameters in Table 1.
Two-Photon Absorption in Photodiodes
/>15
Figure 7 shows the photocurrent when one beam (e
^
) was linearly polarized and the polari‐
zation of the other beam (p
^
) was varied using a quarter-wave plate. The horizontal axis is
the rotation angle of the quarter-wave plate. The polarization of the second beam varied be‐
tween linear, elliptical, and circular in this case. The solid line shows the calculated value
using the parameters in Table 1. The photocurrent had maximum and minimum values
when the second beam was linearly and circularly polarized, respectively. The ratios are

using Eq (8). This ratio is calculated to be 1.53 from the parameters in Table 1, and is consis‐
tent with the measurement.
Figure 8 shows the photocurrent when one beam was circularly polarized while the polari‐
zation of the other beam was varied using a quarter-wave plate between linear, elliptical,
and circular polarization. The unit vectors for circular polarization are σ
^
+
=
1
2
(x
^
+ iy
^
)and
σ
^
−
=
1
2
(x
^
−i y
^
). An arbitrary polarization vector p
^
can be written as a linear combination of
these unit vectors.
p

xyyx
(1 +
|
p
−
|
2
). (23)
We used the relations σ
^
+
⋅σ
^
−
=1andσ
^
+
⋅σ
^
+
=σ
^
−
⋅σ
^
−
=0. β
pe
is independent of p
^

)
sin2θ + χ
″
xxyy
+ 3χ
″
xyyx
(24)
The ratio of the maximum tominimum values is
β
pe
(p
^
=σ
^
+
)
β
pe
(p
^
=σ
^
−
)
=
1
2
(1 +
χ

Polarization direction of the reference beam was varied in four ways. Polarization of the
arbitrarily polarized light can be determined from the four photocurrents of the APD [14].
Several applications require the ability to detect rapid variations in the polarization of an
optical signal. In all conventional polarization measurement methods, the temporal resolu‐
Two-Photon Absorption in Photodiodes
/>17